Over 5000 students were tested on their abilities in Calculus and Physics for a study performed by the Third International Mathematics and Science Study. The testing was separated into four regions of the United States. Some students took the Calculus test, some took the Physics test, and some took both. Assume that the scores represent a random sample for each of the four regions of the U.S.

Test the claim made by Physics teachers that the overall mean U.S. score on the Physics test should be higher than 420. Use a significance level of α = 0.05.